Bring the stock to a simmer. Whisk the ink into half a cup of the hot stock, then return it to the pot. Taste before adding any salt, since ink and stock both contribute seasoning.

Dry the squid well. Heat the oil over medium-high heat in a 14-inch shallow pan. Sear the squid for 2 minutes. Lift out a few attractive rings for the top and leave the rest in the pan.

Reduce heat to medium. Stir in the garlic for 30 seconds, then cook the grated tomatoes until thick and darker, 5–7 minutes. Add paprika and rice, stirring briefly to coat.

Pour in the hot black stock and level the rice. Cook briskly for 7 minutes. Turn the heat down and simmer undisturbed for 10–14 minutes, returning the reserved squid for the final 4 minutes. Add a little hot stock along the edge if the grains are still chalky and the pan is dry.

When the squid is cooked through, the rice tender and the liquid absorbed, take the pan off the heat. Rest 5 minutes and serve with lemon.